A time series of Landsat 8 images at Gulf of Laganas, Zakynthos Island, Greece
Using the Panchromatic band for water column correction
to derive water depth and spectral bottom signature:
Landsat 8 OLIP bandset used for this work

Purple=1Blue=2Green=3PAN=4Red=5NIR=6 and SWIR1=7
Using pan sharpened images in this study
Pan sharpening  using Rstudio Brovey method

work done  november 2016

1 - NO NEED for field data, nor for atmospheric correction
2 - this is demonstrated in this website, using a variety of hyper/multi spectral data
Requirements are
1 - homogeneous water body and atmosphere
2 - some coverage of optically deep water
3 - some coverage of dry land
Problems are
1 - the precision on estimated depth is found wanting, because the noise-equivalent change in radiance  of accessible data is too high for shallow water column correction work 
2 - radiance data should be preprocessed by the provider at level 1 in order to improve S/N ratio
3 - exponential decay: the deeper/darker the bottom, the poorer the performances
I keep digging
until suitable data
become available
 GSD 15m pan-sharpened
The data

most variable atmosphere

TCC deglinted
  • Note the low Blue radiances along the western waterline of Zakynthos island: what's that?
  • This happens at various locations in this scene

Deglinting along Profile_Yellow

Glint regressions are excellent
Deglinting is excellent

Adjacency effect is fairly strong,
several kilometers wide


Calibration under RED ROI

Calibration Blue vs Green
  • Big star: brightest substrate is set to Coral Sand
  • BPL pixels: clearly display as a straight line
  • Reflectance of coral sand is ~2.7 times brighter than this bottom
  • Kblue/Kgreen=0.33  and   Kcoastal/Kgreen=0.35
    • this is Jerlov water type OI+0.9
    • this is very-very clear, just below OIA
  • Deepest bottom detection for this bottom: ~28 m
  • BUT deepest bottom detection for coral sand would be ~47 m
  • Shallowest pixels are at ~7.5 m
    • this sandy slope stretches from 7.5 m down to 28 m
  • Very few pixels in this ROI exhibit darker bottoms
  • Land pixels: they provide a clear view of the SOIL Line assumption
    • Lwcoastal~=26           Lacoastal ~=70
    • Lwblue   ~=20           Lablue     ~=47
    • Lwgreen ~=   2           Lagreen   ~=27
    • Lwpan     ~= 1.5          Lapan     ~=32

Calibration Coastal vs Green

Calibration Blue vs PAN

Calibration under BLUE ROI

Calibration Blue, Green, Red, NIR
  • Small crosses: I have added the BPL pixels of Red_ROI
  • Unchanged: calibration settings are unchanged
  • Identical: optical calibration for the water is quasi identical in both ROIs
  • Very dark: brightest bottoms at Red_ROI are three times brighter than at Blue_ROI
    • this makes for very dark sandy bottoms at Blue_ROI: only 1/8 of the brightness of coral sands!

Calibration Coastal, PAN, Red, and NIR


Ready for Modeling

Retrieved depth in centimeters
see full scene
see legend


B average bottom brightness

Insight on the uncertainty on fake depth over Land areas
In conclusion, the findings suggest that 4SM is as accurate as the commonly used Stumpf’s method, the only difference being the independence of 4SM from previous field data, and the potential to deliver bottom spectral characteristics for further modeling. 4SM thus represents a significant advance in coastal remote sensing potential to obtain bathymetry and optical properties of the marine bottom.
In order to test 4SM against spectral variations of the bottom substrate,
I can enforce a depth over land to apply the water column attenuation from image calibration,
then process these "artificial shallow" pixels to see how well/bad this depth is retrieved.
Result of this exercise 
From very shallow to very deep, the algorithm yields a surprisingly good estimation of depth;
there is hardly any increase in uncertainty as depth increases.
But, wait: this does not include the quantization noise (mmm...)!
I tried including 8_bits quantization of the computation of "artificial" pixels:
absolutely NO change either of av_Z4SM or std_Z4SM for Zland=20m.
GSD=15 m, pan-sharpened. NO smoothing applied.
Just the estimated depth is "noisy", as an expression of
  • the reductive assumption on the Soil Line.
  • the pansharpening process : co-registration MULTI/PAN.
PAN solution
I suppose that this good result is in part a marked benefit of using the PAN band.
Add heterogeneous atmosphere/water
This does not account for the effect of the natural variations of the water/atmosphere optical properties,
which can be very nasty in their own right, and increase dramatically deeper than ~half of the shallow depth range.
Profile Land A along the beach
Profile Land B through town

Profile Land_C through agriculture
Depth applied to land pixels
ZLand=  1 m

ZLand=  2 m
ZLand=  5 m
ZLand=10 m
ZLand=15 m
ZLand=20 m
ZLand=25 m
ZLand=30 m
Average depth retrieved for three profiles
  0.97+-0.20 m...........N=1124
  1.93+-0.23 m
  4.83+-0.40 m
  9.56+-0.47 m
14.43+-0.47 m
19.34+-0.47 m
24.16+-0.40 m
29.01+-0.27 m.............N=553
Zland=1 m==>0.97+-0.2m
Zland=2 m==>1.93+-0.23m
Zland=5 m==>4.83+-0.4m
Zland=10 m==>9.56+-0.47 m
Zland=15 m==>14.43+-0.47m
Zland=20 m==>19.34+-0.47m